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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 732 · 40 questions
TalentJR

How to solve it (Same step every time): In an AP the gap (common difference d) is always the same. nth term = a + (n − 1) × d, where a is the first term. Sum of n terms = n × (first + last) ÷ 2; so 1 + 2 + … + n = n × (n + 1) ÷ 2, and the first n odd numbers add up to n × n.

NameDateTime takenScore ___ / 40
  1. 1.What is the sum of the first 7 terms of the AP 8, 10, 12, …? (a) 196 (b) 20 (c) 105 (d) 98
  2. 2.What is the sum of the first 12 terms of the AP 4, 6, 8, …? (a) 26 (b) 192 (c) 180 (d) 360
  3. 3.What is the missing term in the AP 5, 14, ?, 32, 41? (a) 24 (b) 32 (c) 22 (d) 23
  4. 4.What is the sum of the first 12 terms of the AP 5, 6, 7, …? (a) 16 (b) 126 (c) 252 (d) 132
  5. 5.What is the sum of all the whole numbers from 1 to 43? (a) 946 (b) 947 (c) 903 (d) 1892
  6. 6.What is the 35th term of the AP 18, 27, 36, 45, …? (a) 324 (b) 333 (c) 315 (d) 306
  7. 7.What is the sum of the first 11 terms of the AP 7, 11, 15, …? (a) 319 (b) 594 (c) 47 (d) 297
  8. 8.What is the 13th term of the AP 3, 8, 13, 18, …? (a) 65 (b) 63 (c) 60 (d) 68
  9. 9.What is the sum of the first 8 terms of the AP 1, 7, 13, …? (a) 352 (b) 200 (c) 176 (d) 43
  10. 10.What is the 17th term of the AP 12, 16, 20, 24, …? (a) 64 (b) 76 (c) 68 (d) 80
  11. 11.Which term of the AP 4, 13, 22, 31, … is 247? (a) 29th (b) 28th (c) 27th (d) 30th
  12. 12.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)? (a) 100 (b) 110 (c) 19 (d) 55
  13. 13.What is the sum of all the whole numbers from 1 to 65? (a) 4290 (b) 2145 (c) 2146 (d) 2080
  14. 14.What is the 10th term of the AP 11, 15, 19, 23, …? (a) 51 (b) 47 (c) 36 (d) 40
  15. 15.What is the 33rd term of the AP 5, 14, 23, 32, …? (a) 288 (b) 293 (c) 297 (d) 302
  16. 16.What is the sum of the first 5 terms of the AP 4, 6, 8, …? (a) 80 (b) 12 (c) 45 (d) 40
  17. 17.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)? (a) 552 (b) 45 (c) 529 (d) 276
  18. 18.What is the 10th term of the AP 2, 11, 20, 29, …? (a) 83 (b) 92 (c) 90 (d) 81
  19. 19.What is the 16th term of the AP 9, 16, 23, 30, …? (a) 114 (b) 112 (c) 105 (d) 121
  20. 20.What is the 38th term of the AP 5, 9, 13, 17, …? (a) 153 (b) 157 (c) 148 (d) 152
  21. 21.What is the sum of the first 8 terms of the AP 3, 5, 7, …? (a) 88 (b) 80 (c) 160 (d) 17
  22. 22.What is the 20th term of the AP 20, 27, 34, 41, …? (a) 140 (b) 153 (c) 160 (d) 133
  23. 23.What is the sum of all the whole numbers from 1 to 93? (a) 4372 (b) 4278 (c) 4371 (d) 8742
  24. 24.What is the 17th term of the AP 6, 13, 20, 27, …? (a) 118 (b) 112 (c) 119 (d) 125
  25. 25.What is the 27th term of the AP 15, 21, 27, 33, …? (a) 162 (b) 156 (c) 177 (d) 171
  26. 26.What is the sum of the first 7 terms of the AP 2, 3, 4, …? (a) 35 (b) 70 (c) 36 (d) 8
  27. 27.What is the missing term in the AP 6, 10, 14, ?, 22? (a) 18 (b) 19 (c) 22 (d) 17
  28. 28.What is the 23rd term of the AP 5, 10, 15, 20, …? (a) 115 (b) 110 (c) 120 (d) 116
  29. 29.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)? (a) 11 (b) 42 (c) 21 (d) 36
  30. 30.What is the 17th term of the AP 19, 24, 29, 34, …? (a) 99 (b) 104 (c) 80 (d) 85
  31. 31.What is the sum of all the whole numbers from 1 to 80? (a) 3160 (b) 6480 (c) 3240 (d) 3200
  32. 32.What is the sum of the first 6 terms of the AP 5, 7, 9, …? (a) 15 (b) 66 (c) 60 (d) 120
  33. 33.What is the sum of all the whole numbers from 1 to 56? (a) 1540 (b) 3192 (c) 1568 (d) 1596
  34. 34.What is the 25th term of the AP 20, 28, 36, 44, …? (a) 212 (b) 200 (c) 220 (d) 192
  35. 35.Which term of the AP 4, 6, 8, 10, … is 54? (a) 27th (b) 26th (c) 25th (d) 28th
  36. 36.What is the sum of the first 11 terms of the AP 10, 12, 14, …? (a) 231 (b) 220 (c) 30 (d) 440
  37. 37.What is the sum of the first 9 terms of the AP 8, 11, 14, …? (a) 360 (b) 180 (c) 32 (d) 183
  38. 38.What is the sum of the first 5 terms of the AP 8, 13, 18, …? (a) 180 (b) 95 (c) 90 (d) 28
  39. 39.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)? (a) 272 (b) 136 (c) 31 (d) 256
  40. 40.What is the missing term in the AP 6, 8, ?, 12, 14? (a) 10 (b) 9 (c) 11 (d) 12

Answer key

  1. 98
  2. 180
  3. 23
  4. 126
  5. 946
  6. 324
  7. 297
  8. 63
  9. 176
  10. 76
  11. 28th
  12. 100
  13. 2145
  14. 47
  15. 293
  16. 40
  17. 529
  18. 83
  19. 114
  20. 153
  21. 80
  22. 153
  23. 4371
  24. 118
  25. 171
  26. 35
  27. 18
  28. 115
  29. 36
  30. 99
  31. 3240
  32. 60
  33. 1596
  34. 212
  35. 26th
  36. 220
  37. 180
  38. 90
  39. 256
  40. 10

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